Find the derivative $\frac{d}{dx}\left(x\arcsin\left(x\right)+\sqrt{1-x^2}\right)$ using the sum rule

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$\frac{d}{dx}\left(x\arcsin\left(x\right)\right)+\frac{d}{dx}\left(\sqrt{1-x^2}\right)$

Learn how to solve problems step by step online. Find the derivative d/dx(xarcsin(x)+(1-x^2)^1/2) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\arcsin\left(x\right). The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.